256 Ice in the Sea 



special structure of an ice floe and its past history. The most important of the mechani- 

 cal properties is the elasticity, which is characterized by Young's modulus E and the 

 modulus of rigidity /x. Ice is of course composed of ice crystals and its elasticity is not 

 the same in all stress directions. An ice crystal can be regarded as built up of a large 

 number of thin platelets at right angles to the crystal axis. Deformation at right angles 

 to this axis meets a much smaller resistance than one in the direction of the axis. 

 The different values for Young's modulus shown by different natural samples are 

 probably due to this. Few direct determinations have been made of the elasticity 

 constants for sea ice, but they have been determined more often for fresh water ice by 

 a variety of different methods. The more reliable values for the modulus of elasticity 

 E are those of Reusch, which give 23, 632 kg/cm^. Its variability with the position 

 of the crystal axis relative to the axis of force has also been determined, giving between 

 18, 200 and 38, 300 kg/cm^. E increases with decreasing temperature. 



A more accurate determination of these constants can probably be made indirectly 

 by measurement of the velocity of elastic waves in the ice, and a large number of de- 

 terminations of this type have been made. Ewing, Gray and Thorne (1934) measured 

 this velocity in thin ice rods and found the following values for the elasticity constants: 



Young's modulus E Rigidity modulus fi. Poisson constant a 



9-17 X IQio dyn/cm^ 3.36x lO^odyn/cm^ 0-365 



Seismic measurements of the thickness of the ice on alpine glaciers and in Greenland 

 (Brockamp and Mothes, 1930) have given 



E = 6-82 X lO^o dyn/cm2; ^i = 2-51 X lO^" dyn/cm^; a = 0-361. 



Considering the difference between experimental and natural conditions these values 

 agree quite well. The elastic limit in ice is not large; for river ice Weinberg found 

 0-57 kg/cm^; for granular glacier ice Hess found 0-09 kg/cm^. The plastic limit is, 

 of course, much higher. 



The strength of ice of different origins provides a more useful comparison than the 

 above numerical values and has been used by Makaroff. His measurements show 

 clearly that freshwater ice is of much greater strength than sea ice and that an in- 

 creasing salinity in the water in which it is formed and a higher temperature, makes 

 the sea ice less resistant. Weinberg (1907) investigated the strength of a large number 

 of sea-ice samples and found that the values obtained usually increased with decreas- 

 ing temperature; compared with the values at — 3°C there were increases of 20%, 

 35% and 45% at -10°, -20° and -30°C respectively. 



Investigations of the deformation of ice under the effect of continuous pressure have 

 been made by Andrews, and especially by Royen (1922). From their results, it is worth 

 mentioning that the plastic deformation of ice under the influence of continuous 

 pressure can be expressed by the equation 



pi^T 



1 - T 



where p is the pressure (load) in kg/cm^, T is the duration of this pressure in hours, t 

 is the mean temperature of the ice and k is a constant characteristic for each sample and 



